If[αβγ−α]is the square root of second order unit matrix, Then α,β and γ should satisfy the relation
1−α2+βγ=0
α2+βγ−1=0
1+α2+βγ=0
1−α2−βγ=0
[αβγ−α][αβγ−α]=[1001]⇒[α2+βγ00α2+βγ]=[1001]⇒α2+βγ−1=0